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Volume 19
Issue 3
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Math. Comput. Appl., Volume 19, Issue 3 (December 2014) – 7 articles , Pages 184-262

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352 KiB  
Article
On the Pentanacci Numbers
by Tugba Sarisahin and Ayse Nalli
Math. Comput. Appl. 2014, 19(3), 255-262; https://doi.org/10.3390/mca19030255 - 1 Dec 2014
Cited by 1 | Viewed by 1668
Abstract
In this paper, we give recurrence relation obtained by using from [1] for Pentanacci sequence. Furthermore, we construct generating matrix for P6n, S6n. Finally, we represent relationships between Pentanacci sequence and permanents of certain matrices. [...] Read more.
In this paper, we give recurrence relation obtained by using from [1] for Pentanacci sequence. Furthermore, we construct generating matrix for P6n, S6n. Finally, we represent relationships between Pentanacci sequence and permanents of certain matrices. Full article
507 KiB  
Article
Lacunary Statistical Convergence of Multiple Sequences in Intuitionistic Fuzzy Normed Spaces
by Ekrem Savaş
Math. Comput. Appl. 2014, 19(3), 241-254; https://doi.org/10.3390/mca19030241 - 1 Dec 2014
Cited by 1 | Viewed by 1359
Abstract
In this paper we introduce the notion ideal statistical convergence and ideal lacunary statistical convergence of multiple sequences with respect to the intuitionistic fuzzy norm (μ, v), investigate their relationships, and make some observations about these classes. Full article
199 KiB  
Article
Decomposition Method for Solving a System of Third-Order Boundary Value Problems
by Muhammad Aslam Noor, Khalida Inayat Noor and Asif Waheed
Math. Comput. Appl. 2014, 19(3), 230-240; https://doi.org/10.3390/mca19030230 - 1 Dec 2014
Cited by 1 | Viewed by 1253
Abstract
In this paper, we use the modified decomposition method for solving the system of third-order nonlinear boundary value problems associated with obstacle problems. Some examples of system of third-order nonlinear boundary value problems are given. The comparison of the results obtained by modified [...] Read more.
In this paper, we use the modified decomposition method for solving the system of third-order nonlinear boundary value problems associated with obstacle problems. Some examples of system of third-order nonlinear boundary value problems are given. The comparison of the results obtained by modified decomposition method with modified variation of parameters method is also given. Results are also shown graphically that demonstrate the nature of the obstacles in particular problems. The results are very encouraging indicating the reliability and efficiency of the technique. Full article
364 KiB  
Article
A Network Traffic Prediction Model Based on Quantum Inspired Pso and Wavelet Neural Network
by Kun Zhang
Math. Comput. Appl. 2014, 19(3), 218-229; https://doi.org/10.3390/mca19030218 - 1 Dec 2014
Cited by 1 | Viewed by 1601
Abstract
Network traffic flow prediction model is fundamental to the network performance evaluation and the design of network control scheme which is crucial for the success of high-speed networks. Aiming at shortcoming of the conventional network traffic time series prediction model and the problem [...] Read more.
Network traffic flow prediction model is fundamental to the network performance evaluation and the design of network control scheme which is crucial for the success of high-speed networks. Aiming at shortcoming of the conventional network traffic time series prediction model and the problem that BP training algorithms easily plunge into local solution, a network traffic prediction model based on wavelet neural network and PSO-QI is presented in the paper. Firstly, the quantum principle obtained from Quantum PSO(QPSO)has been combined with standard PSO to form a new hybrid algorithm called PSO with Quantum Infusion(PSO-QI). Then, the parameters of wavelet neural network were optimized with PSO-QI and the time series of network traffic data was modeled and predicted based on wavelet neural network and PSO-QI. Experiments showed that PSOQI-wavelet neural network has better precision and adaptability compared with the traditional neural network. Full article
264 KiB  
Article
Special Finite Difference Method for Singular Perturbation Problems with One-End Boundary Layer
by K. Phaneendra, K. Madhulatha and Y.N. Reddy
Math. Comput. Appl. 2014, 19(3), 208-217; https://doi.org/10.3390/mca19030208 - 1 Dec 2014
Viewed by 1573
Abstract
In this paper, we have presented a special finite difference method for solving a singular perturbation problem with layer behaviour at one end. In this method, we have used a second order finite difference approximation for the second derivative, a modified second order [...] Read more.
In this paper, we have presented a special finite difference method for solving a singular perturbation problem with layer behaviour at one end. In this method, we have used a second order finite difference approximation for the second derivative, a modified second order upwind finite difference approximation for the first derivative and a second order average difference approximation for y to reduce the global error and retaining tridiagonal system. Then the discrete invariant imbedding algorithm is used to solve the tridiagonal system. This method controls the rapid changes that occur in the boundary layer region and it gives good results in both cases i.e., h ≤ ε and ε << h. The existence and uniqueness of the discrete problem along with stability estimates are discussed. Also we have discussed the convergence of the method. We have presented maximum absolute errors for the standard examples chosen from the literature. Full article
302 KiB  
Article
New Exact Analytical Solutions for the General KdV Equation with Variable Coefficients
by Bao-Jian Hong and Dian-Chen Lu
Math. Comput. Appl. 2014, 19(3), 194-207; https://doi.org/10.3390/mca19030194 - 1 Dec 2014
Cited by 1 | Viewed by 1648
Abstract
In this paper, a general algebraic method based on the generalized Jacobi elliptic functions expansion method, the improved general mapping deformation method and the extended auxiliary function method with computerized symbolic computation is proposed to construct more new exact solutions of a generalized [...] Read more.
In this paper, a general algebraic method based on the generalized Jacobi elliptic functions expansion method, the improved general mapping deformation method and the extended auxiliary function method with computerized symbolic computation is proposed to construct more new exact solutions of a generalized KdV equation with variable coefficients. As a result, eight families of new generalized Jacobi elliptic function wave solutions and Weierstrass elliptic function solutions of the equation are obtained by using this method, some of these solutions are degenerated to soliton-like solutions, trigonometric function solutions in the limit cases when the modulus of the Jacobi elliptic functions m → 1 or 0, which shows that the general method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics. Full article
238 KiB  
Article
Analysis and Controlling of Hopf Bifurcation for Chaotic Van Der Pol-Duffing System
by Ping Cai, Jia-Shi Tang and Zhen-Bo Li
Math. Comput. Appl. 2014, 19(3), 184-193; https://doi.org/10.3390/mca19030184 - 1 Dec 2014
Cited by 3 | Viewed by 1356
Abstract
Analysis and controlling of bifurcation for a class of chaotic Van der Pol- Duffing system with multiple unknown parameters are conducted. The stability of the equilibrium of the system is studied by using Routh-Hurwitz criterion, and the critical value of Hopf bifurcation is [...] Read more.
Analysis and controlling of bifurcation for a class of chaotic Van der Pol- Duffing system with multiple unknown parameters are conducted. The stability of the equilibrium of the system is studied by using Routh-Hurwitz criterion, and the critical value of Hopf bifurcation is investigated. Based on the center manifold theory and normal form reduction, the stability index of bifurcation solution is given. Linear and nonlinear washout filter feedback controllers are designed respectively to control the bifurcation critical value and the amplitude of the limit cycle. Numerical simulation results are presented to illustrate analytical results found. Full article
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